Find the domain for
`" " y=sin^(-1)(log_(2)(x^(2)/2))`.

Options

A. `[-2,-1]`
B. [1,2[
C. `[-2,-1] cup [1,2]`
D. none of these

Answer

C

Explanation

Since the domain of `sin^(-1)x ` is [-1,1]. Therefore , `f(x)=sin^(-1){log_(2)((x^(2))/(2))}` exists , if
`-1 le log_(2)(x^(2)//2) le 1implies 2^(-1) le (x^(2))/(2) le 2^(1)`
`implies 1 le x^(2) le 4 implies 1 le |x| le 2 implies x in [-2,-1] cup [1,2]`
Hence , the domain of f(x) is `[-2,-1] cup [1,2]`